CN106410783B - A kind of Power System Shortcuts current attenuation calculation method based on coordinate transform - Google Patents
A kind of Power System Shortcuts current attenuation calculation method based on coordinate transform Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract
The Power System Shortcuts current attenuation calculation method based on coordinate transform that the present invention relates to a kind of, comprising the following steps: 1) obtain initial nodal voltage equation, initial nodal voltage equation is modified, and obtains revised nodal voltage equation；2) real number expression is carried out to revised nodal voltage equation；3) network equation for obtaining rotating electric machine by coordinate transform according to the nodal voltage equation after real number, the equivalent Injection Current equation of generator and motor corresponding node is obtained according to the network equation of rotating electric machine respectively；4) the decaying potential of generator and motor is obtained respectively according to the accounting equation of generator and motor potential and rotary electric machine electric current before short circuit；5) according to the short-circuit voltage of generator and the decaying each node of potential calculation of motor；6) short circuit current of short-circuited node is obtained.Compared with prior art, the present invention has many advantages, such as to consider that comprehensive, calculating is accurate, closing to reality.
Description
Technical field
The present invention relates to a kind of short circuit current acquisition methods, short more particularly, to a kind of electric system based on coordinate transform
Road current attenuation calculation method.
Background technique
Currently, the conventional calculation of short-circuit current that domestic electrical enterprise uses only calculates periodic component of short-circuit current, it cannot
Calculate the attenuation of periodic component of short-circuit current, although and the calculation of short-circuit current curve method that traditionally uses can calculate it is short
The attenuation of road current cycle component, but load is equivalent to static load by this method, uses prior defined power train
It unites typical operation modes rather than actual motion state.
When common commercial power system simulation software of power grid enterprises calculates short circuit current, PSASP ignores the influence of load；
The synthetic load containing induction conductivity can be considered in BPA program, but can only the initial virtual value of calculating cycle component；PSS/E
Although BKDY module can calculate the attenuation of periodic component of short-circuit current, load is equivalent to static negative by this method
Lotus, the multilayer output feedback network function of above-mentioned simulation software, being capable of calculating cycle components by the differential equation of solution whole system
Decaying, however data preparation is cumbersome, calculation amount is bigger than normal, is generally not used for the engineering calculation of short circuit current.
Summary of the invention
Comprehensive, calculating is considered it is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of
Accurately, the Power System Shortcuts current attenuation calculation method based on coordinate transform of closing to reality.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of Power System Shortcuts current attenuation calculation method based on coordinate transform, comprising the following steps:
1) Load flow calculation is carried out according to power grid actual motion state, obtains initial nodal voltage equation, it is negative according to static state
The ratio of lotus and dynamic load is modified initial nodal voltage equation, obtains revised nodal voltage equation；
2) real number expression is carried out to revised nodal voltage equation, the nodal voltage equation after obtaining real number；
3) network equation for obtaining rotating electric machine by coordinate transform according to the nodal voltage equation after real number, according to rotation
The network equation of rotating motor obtains the equivalent Injection Current equation of generator and motor corresponding node respectively；
4) it is obtained respectively according to the accounting equation of generator and motor potential and rotary electric machine electric current before short circuit
Take the decaying potential of generator and motor；
5) according to the decaying potential of generator and motor, the equivalent each node of Injection Current equation calculation of corresponding node
Short-circuit voltage；
6) short circuit current of short-circuited node is obtained according to the short-circuit voltage of the node voltage of short-circuited node and its adjacent node.
The revised nodal voltage equation are as follows:
Ykk=YNkk+yLD.k
Wherein,For node Injection Current column vector,For node voltage column vector, Y is node admittance matrix, YkkFor section
Self-admittance of the point admittance matrix Y in node k, YNkkFor the node admittance matrix Y before amendmentNIn the self-admittance of node k, yLD.kFor section
The static load equivalent admittance of point k.
Nodal voltage equation after the real number are as follows:
Wherein, i, j are that different bus nodes are numbered, Gij、BijNondiagonal element in respectively revised admittance matrix Y
The real and imaginary parts of element, Vjx、VjyThe respectively real and imaginary parts of the node voltage plural form of node j, I 'ix、I′iyRespectively
The real and imaginary parts of the node Injection Current plural form of node i, n are bus nodes sum；
In the step 3), the expression formula of the network equation of rotating electric machine are as follows:
Wherein, I "ix、I″iyThe respectively real and imaginary parts of rotating electric machine node i equivalence Injection Current plural form, Gix、
Giy、Bix、BiyThe respectively self-admittance second order submatrix correction factor of rotating electric machine node i, GijAnd BijIt is respectively revised
The real and imaginary parts of off-diagonal element, G in admittance matrix Yii、BiiThe real part of diagonal entry in respectively node admittance matrix Y
And imaginary part, Vjx、VjyThe respectively real and imaginary parts of the node voltage plural form of node j.
When rotating electric machine is generator, the expression formula phase of network equation expression formula and the network equation of rotating electric machine
Together, in formula:
Wherein, Ria、Xiq、X″id、X″iqThe respectively internal resistance, the steady-state reactance of q axis of node i institute running fire motor and d, q axis
Transient state reactance, Vi、δiVRespectively the node voltage virtual value of node i institute running fire motor and phase angle, Δ Vi、δViRespectively generate electricity
The vertical component and horizontal component of electromechanical drop of pressure, Pi、QiFor active power and reactive power that generator is supplied to system, δiFor hair
The angle of rotor q axis and x-axis；
Then have, the equivalent Injection Current equation of generator corresponding node are as follows:
Wherein, I "ix、I″iyThe respectively real and imaginary parts of generator node i equivalence Injection Current plural form, E "iq、
E″idFor d, q axis after motor short circuit time transient potential, Cix1、Cix2、Ciy1、Ciy2For generator network equation parameter, RiaFor section
The internal resistance of point i institute running fire motor, δiFor the angle of generator amature q axis and x-axis, X "id、X″iqRespectively node i institute running fire motor
D, q axis subtranient reactance.
When rotating electric machine is motor, the expression formula phase of network equation expression formula and the network equation of rotating electric machine
Together, also,
When motor is double-deck induction motor, then have:
When motor is single mouse cage induction conductivity, then have:
Wherein, RiaFor resistance in the motor in node i, X'iFor the motor transient state reactance in node i, X "iFor node
Motor subtranient reactance on i, ωi=1-siFor motor angle speed, siFor revolutional slip.
When rotating electric machine is double-deck induction motor, equivalent Injection Current equation are as follows:
ωi=1-si
Wherein, E "M-id、E″M-iqRespectively connected double-deck induction motor d, q axis of node i time transient potential, Cix、Ciy
For network equation parameter, RiaBy the internal resistance of node i even double-deck induction motor, X 'iFor the double mouse cage induced electricities of company of node i institute
The motor transient state reactance of motivation, ωiFor double-deck induction motor angular speed, siFor revolutional slip；
When rotating electric machine is single mouse cage induction conductivity, equivalent Injection Current equation are as follows:
ωi=1-si
Wherein, E'M-iq、E'M-idRespectively node i q, d axis transient potential for connecting single mouse cage induction conductivity, Cix、Ciy
For network equation parameter, Ria、X'iThe respectively node i internal resistance, the transient state reactance that connect single mouse cage induction conductivity, ωiFor single mouse
Cage induction motor angular speed, siFor single mouse cage motor slip.
In the step 4), generator decaying potential equation includes the attenuation type of generator short circuit d axis time transient potential
With the attenuation type of q axis time transient potential,
The attenuation type of the generator short circuit q axis time transient potential are as follows:
Wherein, iid0For moment stator winding d shaft current, X before generator short circuitid、X′id、X″idRespectively generator d axis
Steady-state reactance, transient state reactance and subtranient reactance, T 'id、T″idDecay for generator d axis transient state component and time transient state component
Time constant, XieFor the ratio of moment generator voltage and generator terminal electric current after generator short circuit, E "iq0Before generator short circuit
Moment q axis transient potential, E "iqFor q axis transient potential after generator short circuit.
When generator q axis direction is there are two Damper Winding, the attenuation type of the generator short circuit d axis time transient potential
Are as follows:
Wherein, iiq0For moment stator winding q shaft current, X before generator short circuitiq、X′iq、X″iqRespectively generator q axis
Steady-state reactance, transient state reactance and subtranient reactance, T 'iq、T″iqDecay for generator q axis transient state component and time transient state component
Time constant, E "idFor d axis transient potential, E " after generator short circuitid0For moment d axis transient potential before generator short circuit,
When generator q only one Damper Winding of axis direction, the decaying of the generator short circuit d axis time transient potential
Formula are as follows:
In the step 4), motor decaying potential equation includes double-deck induction motor decaying potential equation and list
Mouse cage induction conductivity decaying potential equation,
The attenuation type of the double-deck induction motor short circuit d axis time transient potential and the decaying of q axis time transient potential
Formula are as follows:
Wherein, iiq0、iid0Moment stator winding q, d shaft current, X respectively before motor short circuitiq、X′iq、X″iqRespectively
Steady-state reactance, transient state reactance and the subtranient reactance of motor q axis, Xid、X′id、X"idThe respectively stable state electricity of motor d axis
Anti-, transient state reactance and subtranient reactance, T 'iq、T″iqTime for motor q axis transient state component and time transient state component decaying is normal
Number, T 'id、T″idFor the time constant of motor d axis transient state component and time transient state component decaying, E "id、E″iqFor motor short circuit
D, q axis time transient potential afterwards, E "id0、E″iq0For moment d, q axis transient potential, X before motor short circuitieFor wink after motor short circuit
Between terminal voltage of motor and generator terminal electric current ratio；
The attenuation type of single mouse cage induction conductivity short circuit d axis time transient potential and the decaying of q axis time transient potential
Formula are as follows:
Wherein, E'iq、E'idAnd E'iq0、E'id0Respectively after motor short circuit and short circuit before moment d, q axis transient potential.
The step 4) specifically includes the following steps:
41) the equivalent Injection Current of rotating electric machine transcient short circuit time is obtained according to generator, the motor potential before short circuit；
42) according to moment each node after the network equation acquisition short circuit after the equivalent Injection Current and real number of transcient short circuit time
Voltage；
43) it is obtained according to the voltage of moment each node after the potential of each generator and motor before short circuit and short circuit each
The Injection Current of moment, i.e. rotary electric machine electric current, the calculating of the rotary electric machine electric current after rotating electric machine short circuit
Equation includes:
Generator unit stator electric current equation:
Double-deck induction motor stator current equation:
Single mouse cage induction conductivity stator current equation:
Wherein, I 'ix、I′iyThe respectively real and imaginary parts of the node Injection Current plural form of node i, Vix、ViyFor rotation
The real and imaginary parts of rotating motor set end voltage plural form, Gix、Giy、Bix、BiyThe respectively self-admittance two of rotating electric machine node i
Rank submatrix correction factor, Cix、CiyFor motor network equation parameter, Cix1、Cix2、Ciy1、Ciy2For generator network equation ginseng
Number, Ei′d、Ei′qFor d, q axis transient potential, E " after motor short circuitid、E″iqFor d, q axis after motor short circuit time transient potential；
44) it is calculated between the rotating electric machine and short dot according to the set end voltage of moment rotating electric machine and Injection Current after short circuit
Electrical distance Xie:
45) according to electrical distance Xie, generator and motor decaying potential equation obtain declining after rotating electric machine short circuit
Powered down gesture.
In the step 6), the short circuit current of short-circuited node are as follows:
Wherein, f is short dot, and m is short dot circuitry number,For after short circuit with short dot f connected node voltage, YifFor
The transadmittance of short dot f and node i.
Compared with prior art, the invention has the following advantages that
The present invention uses nodal voltage equation, considers various generator models and dynamic load model using coordinate transform
The equivalent Injection Current that (dynamic load uses various types of induction motor models) calculates corresponding node, finally by solution
Network equation (i.e. nodal voltage equation) obtains each node voltage after short circuit, and then calculates short circuit current attenuation, and existing
Technology is compared, the present invention because use d axis, q axis split axle processing, it may be considered that generator, induction conductivity type it is neat
Entirely, make to consider that the system short-circuit current attenuation after dynamic load influence is calculated closer to actual conditions.
Calculating for short circuit current meter and short circuit current can decline while considering generator, dynamic load contribution in this way
Subtract, to adjust protective relaying device in selection electrical equipment and current-carrying conductor, determine that measures for limiting short-circuit current etc. is done
More accurate judgement out guarantees to avoid unnecessary waste while equipment safety.
Detailed description of the invention
Fig. 1 is the access figure of generator and load equivalent circuit.
Fig. 2 is coordinate conversion relation schematic diagram.
Fig. 3 is that the network structure of IEEE9 system and trend before short circuit are distributed.
Dynamic load current cycle component decaying schematic diagram is considered when Fig. 4 is bus BusA three-phase shortcircuit.
Current cycle component decaying schematic diagram under static load when Fig. 5 is bus BusA three-phase shortcircuit.
Dynamic load current cycle component decaying schematic diagram is considered when Fig. 6 is bus Bus1 three-phase shortcircuit.
Current cycle component decaying schematic diagram under static load when Fig. 7 is bus Bus1 three-phase shortcircuit.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
Embodiment:
Consider that the short circuit current that operation states of electric power system influences is decayed in fact using coordinate transform the invention proposes a kind of
Use calculation method.This method uses nodal voltage equation, using coordinate transform, according to the operating status before Power System Shortcuts,
Rotating electric machine corresponding node Injection Current in calculate node voltage equation finally solves network equation (i.e. nodal voltage equation),
And then calculate short circuit current attenuation.
Specific implementation step and key point are as follows:
(1) Load flow calculation is first carried out according to power grid actual motion state, obtains the nodal voltage equation of short-circuit preceding Load flow calculation
Such as formula (1), each node voltage and each branch power can be obtained by solving formula (1) corresponding Load flow calculation power equation；
(2) nodal voltage equation for correcting Load flow calculation is formula (2)；
In formula (1), (2)For node voltage column vector；For node Injection Current column vector, the former composition member
Element is the i in Fig. 1, and the constitution element of the latter is the i' in Fig. 1；YN, Y be node admittance matrix, only load section between the two
The corresponding diagonal entry (i.e. the corresponding self-admittance element of load bus) of point is different, and the latter is on the basis of the former corresponding element
Add the y in Fig. 1LD.k(i.e. the corresponding admittance of static load), as shown in Figure 1.
(3) more network equation (nodal voltage equation) real numberization is expressed
Each vector parameter is write as complex representation and can be had in network equation (2)Y=G+jB,It is right
It carries out real number handle arbitrary node i equation matrix form such as formula (3) shown in:
(4) Injection Current and network equation of generator corresponding node are asked with coordinate transform
When calculating decaying short circuit current with electric power network equation (3), node Injection Current complex vectorOnly generator section
The electric current of point and induction-motor load node is not zero, remaining node is zero.
For the motor in node i, first by the voltage equation (voltage and current of rotating electric machine d, q establishment of coordinate system
Forward direction uses Generator convention) it is coordinately transformed (relationship is as shown in Figure 2 between coordinate), obtain the electric rotating under x, y coordinate system
Machine stator current equation；Then x is substituted into, the real number network equation (3) of y coordinate system merges to obtain network equation (4):
In Fig. 2:Wherein Ria、Xid、XiqPoint
It Wei not the interior resistance of rotating electric machine and d, q axis steady-state reactance, δ in node iivFor the angle of the motor set end voltage in node i.
The derivation process of network equation (4) are as follows:
Generator and motor magnetic linkage formula all calculate under d, q axis coordinate system respectively.But it carries out in systems
It must be under unified coordinate system, and due to the rotor-position of motor in system general each not phase when calculation of short-circuit current
Together, it is therefore desirable to which unified reference axis x, y is set in total system, so as to the connection established between each motor d, q axis operating parameter
System.If the reference axis of synchronous rotary is selected as coincidenting with x axis, the angle δ of rotor q axis and x-axis, as rotor is exhausted
Diagonally, shown to the transformation matrix C such as formula (1-1) of x, y coordinate system from d, q coordinate system.
In formula:Wherein RaIt is electric in rotating electric machine
Resistance, XqFor rotating electric machine q axis steady-state reactance, δVFor the angle of motor set end voltage.
It can thus be concluded that out between x, y coordinate system and d, q coordinate system shown in transformational relation such as formula (1-2).
When meter and Generator Damping winding influence, generator node is calculated to the Injection Current of power grid, it must be by being fixed on electricity
D, q establishment of coordinate system voltage equation on machine rotor, matrix form are shown below.
To formula (2-1) equal sign both sides with the Matrix C multiplied by coordinate transform, the generator unit stator electricity under x, y coordinate system can be obtained
Stream is as shown in formula.
Each parameter such as formula (2-3), (2-4) are shown in formula,
Wherein, RGa、X"Gd、X"GdThe interior resistance of rotating electric machine and d, q axis time steady-state reactance respectively in node i.
According to real number network equation, it is known that if node i is generator node, node Injection Current is generator
Stator current, node voltage are set end voltage.Stator current formula (2-2) is substituted into real number network equation (3) left end,
In item related with set end voltage move on to right end and merge with similar terms, network equation (2-5) can be obtained
Wherein parameter Gix、Giy、Bix、BiyIt is identical as formula (2-3).
Wherein any generator node Injection Current I "i=I "ix+jI"iyIt can be collectively expressed as shown in formula (2-6).
In formula: E "id、E"iqGenerator time transient potential respectively in node i, other four parameters such as formula (2-4) institute
Show.
(5) Injection Current of motor corresponding node is sought with coordinate transform
To be consistent with synchronous generator, Generator convention is set by induction conductivity generator terminal electric current positive direction, then
Network equation (2-5) is applicable not only to generator, and equally applicable for motor, but parameter calculation formula therein and hair
The difference of motor.
For double-deck induction motor, corresponding (4) formula, the parameter G of any motor nodeix、Giy、Bix、BiyIt can unify
It is expressed as shown in formula (8).Wherein, RiaFor resistance in the motor in node i, X "iFor the motor time transient state electricity in node i
It is anti-, ωi=1-si(s is revolutional slip).
Any motor node Injection Current in same up-to-date style (4)It can be collectively expressed as shown in formula (9).
In formula: E "id、E"iqMotor time transient potential respectively in node i, other four parameters such as following formula (10) institute
Show.Wherein, Ria、X"i、ωiSame formula (8).
For single mouse cage induction conductivity, corresponding (4) formula, the parameter G of any motor nodeix、Giy、Bix、BiyIt can unify
It is expressed as shown in formula (11).Wherein, RiaFor resistance in the motor in node i, X'iFor the motor transient state electricity in node i
It is anti-.
Any generator node Injection Current in same up-to-date style (4)It can be collectively expressed as shown in formula (12).
In formula: E'id、E'iqMotor d, q transient potential respectively in node i, other four parameters such as following formula (13)
It is shown.Wherein, Ria、X'iSame formula (11).
(6) calculating of generator decaying potential
The Injection Current of any time rotating electric machine after calculating short circuit, by formula (2-6), formula (9) and formula (12) it is found that first
Need to calculate the motor potential of any time.
For the generator in node i, shown in the decay calculation such as formula (14) of short circuit q axis time transient potential.
In formula: iid0For moment stator winding d shaft current before generator short circuit；Xid、X'id、X"idRespectively generator is steady
State reactance, transient state reactance, subtranient reactance；T'id、T"idRespectively d axis transient state component, the time of secondary transient state component decaying are normal
Number；XieFor the quotient of moment generator voltage and generator terminal electric current after the short circuit that is calculated based on node admittance matrix, E "iq0It is short for q axis
Moment time transient potential before road.
For d axis time transient potential, when q axis is there are two when Damper Winding, secondly decaying such as formula (15) institute of transient potential
Show.
In formula: iiq0For moment stator winding q shaft current before generator short circuit；Xiq、X'iq、X"iqRespectively generator is steady
State reactance, transient state reactance, subtranient reactance；T'iq、T"iqRespectively q axis transient state component, the time of secondary transient state component decaying are normal
Number；XieFor the quotient of moment generator voltage and generator terminal electric current after the short circuit that is calculated based on node admittance matrix；E"id0It is short for d axis
Moment time transient potential before road.
And when generator q only one Damper Winding of axis direction, decaying such as formula (16) institute of d axis time transient potential
Show.
The same formula of parameter (15) in formula.
(7) calculating of motor decaying potential
For the double-deck induction motor in node i, after short circuit the decaying of d, q axis transient potential respectively as formula (17),
(18) shown in.Wherein, E "iq0、E"id0Respectively motor short circuit moment d, q axis transient potential, the same formula of other parameters (14).
For single mouse cage induction conductivity in node i, after short circuit shown in the decaying such as formula (19) of d axis transient potential.Its
In, E'iq0For motor short circuit moment d axis transient potential, the same formula of other parameters (14).
(8) network equation is solved, voltage after short circuit is calculated.
It can be seen that firstly the need of in short circuit moment calculating X occurs for potential to be calculated by motor decaying potential calculation formulaie
Value.After the Injection Current of each rotating electric machine is calculated, motor set end voltage V can be found out according to network equation (3)ix、Viy；
And according to rotary electric machine current equation (shown in generator such as formula (21)；Double, single squirrel cage motor respectively as formula (22),
(23) shown in) find out stator current I'ix、I'iy.The then parameter X of rotating electric machineie, calculation formula is such as shown in (24).
In this way, the generator potential and motor potential of any time Δt after short circuit can be calculated according to decaying potential equation,
Any time Δt Injection Current is calculated using coordinate transform, solve network equation can obtain it is short-circuit after any time Δt voltage.
(9) short circuit current is solved
In calculation of short-circuit current, if it is possible to find out the injection of any time generator and dynamic load to electric power networks
Electric currentSo electric power networks can be solved using equations of network (2) to obtainUsing with short dot connected node voltage
With transadmittance product, obtains short dot and be connected the short circuit current of all branches supply, the short circuit current for summing always.
Any time node voltage and Injection Current are acquired according to above-mentioned calculating process, is then found out arbitrarily using formula (25)
Time Δt short circuit current calculates short circuit current attenuation.
In formula: f is short dot, and m is short dot circuitry number,For after short circuit with short dot connected node voltage, YifIt is short
The transadmittance of waypoint and node i.
In addition, the calculation method needs to separate total load into one when considering dynamic load calculation decaying short circuit current
It is allocated as dynamic load.For power component, directly it is divided into P according to the ratio of static load and dynamic load0(static load)
With P (dynamic load), P0+ P=PLD；And for reactive component, it be according to the corresponding active power of dynamic load, load factor and electricity
Motivation stable state equivalent circuit calculates the corresponding stable state reactive component Q of motor, then total load or burden without work QLDSubtract dynamic load
Remainder is the idle Q of static load after the idle Q needed0, i.e. Q0=QLD- Q, the in this way system after consideration dynamic load
Trend and original consistent.
The short circuit current decaying for considering dynamic load characteristic is calculated using the above method.This method acquired results and calculating are bent
The calculated result of collimation method is compared, and uses electromechanical transient simulation calculated result as the judgement of its reasonability and correctness.
Electromechanical transient simulation calculation method accurately considers the quasi steady state model of generator, the differential equation and network generation by generator
Number solving simultaneous equations, so its data preparation, modeling it is more complex, calculate needed for memory and operand it is larger, electromechanical transient
Emulated computation method is generally not as short circuit current conventional Calculation Method, but it can be used to check other calculation of short-circuit current sides
The accuracy of method.
Select IEEE9 system as applicating example of the invention here, it is negative according to 40% dynamic to the load of bus BusA
The ratio of+60% static load of lotus is allocated, remaining load is still static load.Respectively to system median generatrix BusA and bus
Bus1 accounts for the three short circuit current decay calculation of dynamic load characteristic, and the calculated result for listing file names with calculated curve method is made
For comparison.Trend distribution before the network structure of IEEE9 system and short circuit as shown in figure 3, calculated result such as table 1, table 2 and Fig. 4 extremely
Shown in Fig. 7.
Table 1 considers periodic component of short-circuit current attenuation verses before and after dynamic load characteristic
Table 2 considers periodic component of short-circuit current attenuation verses before and after dynamic load characteristic
It can be seen that from table 1, table 2 and Fig. 4 to Fig. 7 when not considering dynamic load, Practical Method and electromechanical transient simulation
As a result generally relatively, accuracy with higher.In contrast, the calculated result of traditional calculations curve is more conservative,
Short dot is different, and phase rate is also different.If short circuit occurs in bus Bus1, phase rate is all larger than 10%；If short circuit occurs
In bus BusA, phase rate is all within 10%.So if checking opening for breaker with the calculated result of traditional calculations curve
Power-off stream, still there is certain safety margin, but seems overly conservative in certain short dots (the bus Bus1 in such as this example),
Be unfavorable for excavation breaker cut-offs potentiality.
After considering dynamic load characteristic, the calculating of Practical Method and electromechanical transient simulation has preferable in different moments
The goodness of fit, in the time range 0-0.1s of research, phase rate is within ± 4%；It is real and after considering dynamic load characteristic
Resulting motor flow increasing effect highly significant is calculated with calculating method, transcient short circuit time increases when short dot is closer from dynamic load
Rate reaches 15% or more, is then gradually reduced, until 0.1s is reduced within 10%；When short dot farther out from dynamic load when,
Magnification reaches 5% or more, and then gradually smaller within 1%, attenuation meets theoretical rule.
It is analyzed by applicating example, it may be said that the bright short circuit current proposed by the present invention for considering dynamic load characteristic is decayed real
With the calculated result of calculation method accuracy with higher, the goodness of fit of short circuit current attenuation curve and electromechanical transient also compared with
It is good.It can be consequently used for considering the grid short circuit current attenuation characteristic research of dynamic load, and after considering dynamic load characteristic
Acquired results more meet power grid actual short current conditions when not considering.
Claims (9)
1. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform, which comprises the following steps:
1) Load flow calculation is carried out according to power grid actual motion state, obtains initial nodal voltage equation, according to static load and
The ratio of dynamic load is modified initial nodal voltage equation, obtains revised nodal voltage equation；
2) real number expression is carried out to revised nodal voltage equation, the nodal voltage equation after obtaining real number；
3) network equation for obtaining rotating electric machine by coordinate transform according to the nodal voltage equation after real number, according to electric rotating
The network equation of machine obtains the equivalent Injection Current equation of generator and motor corresponding node respectively；
4) hair is obtained according to the accounting equation of generator and motor potential and rotary electric machine electric current before short circuit respectively
The decaying potential of motor and motor, the step 4) specifically includes the following steps:
41) the equivalent Injection Current of rotating electric machine transcient short circuit time is obtained according to generator, the motor potential before short circuit；
42) electricity of moment each node after short circuit is obtained according to the network equation after the equivalent Injection Current and real number of transcient short circuit time
Pressure；
43) each rotation is obtained according to the voltage of moment each node after the potential of each generator and motor before short circuit and short circuit
The Injection Current of moment after electric motor short circuit, i.e. rotary electric machine electric current, the accounting equation of the rotary electric machine electric current
Include:
Generator unit stator electric current equation:
Double-deck induction motor stator current equation:
Single mouse cage induction conductivity stator current equation:
Wherein, I 'ix、I′iyThe respectively real and imaginary parts of the node Injection Current plural form of node i, Vix、ViyFor electric rotating
The real and imaginary parts of machine set end voltage plural form, Gix、Giy、Bix、BiyRespectively self-admittance second order of rotating electric machine node i
Matrix correction factor, Cix、CiyFor motor network equation parameter, Cix1、Cix2、Ciy1、Ciy2For generator network equation parameter,
E′id、E′iqFor d, q axis transient potential, E " after motor short circuitid、E″iqFor d, q axis after motor short circuit time transient potential；
44) electricity between the rotating electric machine and short dot is calculated according to the set end voltage of moment rotating electric machine and Injection Current after short circuit
Gas distance Xie:
45) according to electrical distance Xie, generator and motor decaying potential equation obtain the decaying electricity after rotating electric machine short circuit
Gesture；
5) according to the decaying potential of generator and motor, corresponding node the equivalent each node of Injection Current equation calculation it is short
Road voltage；
6) short circuit current of short-circuited node, short circuit are obtained according to the short-circuit voltage of the node voltage of short-circuited node and its adjacent node
The short circuit current of node are as follows:
Wherein, f is short dot, and m is short dot circuitry number,For after short circuit with short dot f connected node voltage, YifFor short dot
The transadmittance of f and node i.
2. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 1, special
Sign is, the revised nodal voltage equation are as follows:
Ykk=YNkk+yLD.k
Wherein,For node Injection Current column vector,For node voltage column vector, Y is node admittance matrix, YkkIt is led for node
Receive self-admittance of the matrix Y in node k, YNkkFor the node admittance matrix Y before amendmentNIn the self-admittance of node k, yLD.kFor node k
Static load equivalent admittance.
3. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 1, special
Sign is, the nodal voltage equation after the real number are as follows:
Wherein, i, j are that different bus nodes are numbered, Gij、BijThe reality of off-diagonal element in respectively revised admittance matrix Y
Portion and imaginary part, Vjx、VjyThe respectively real and imaginary parts of the node voltage plural form of node j, n are bus nodes sum.
4. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 1, special
Sign is, in the step 3), the expression formula of the network equation of rotating electric machine are as follows:
Wherein, I "ix、I″iyThe respectively real and imaginary parts of rotating electric machine node i equivalence Injection Current plural form, Gix、Giy、
Bix、BiyThe respectively self-admittance second order submatrix correction factor of rotating electric machine node i, GijAnd BijRespectively revised admittance
The real and imaginary parts of off-diagonal element, G in matrix Yii、BiiThe real part and void of diagonal entry in respectively node admittance matrix Y
Portion, Vjx、VjyThe respectively real and imaginary parts of the node voltage plural form of node j.
5. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 4, special
Sign is that, when rotating electric machine is generator, network equation expression formula is identical as the expression formula of the network equation of rotating electric machine,
In formula:
Wherein, Ria、Xiq、X″id、X″iqThe respectively internal resistance, the steady-state reactance of q axis of node i institute running fire motor and d, q axis time transient state
Reactance, Vi、δiVRespectively the node voltage virtual value of node i institute running fire motor and phase angle, Δ Vi、δViRespectively power generation is electromechanical
The vertical component and horizontal component of drop of pressure, Pi、QiFor active power and reactive power that generator is supplied to system, δiFor generator
The angle of rotor q axis and x-axis；
Then have, the equivalent Injection Current equation of generator corresponding node are as follows:
Wherein, I "ix、I″iyThe respectively real and imaginary parts of generator node i equivalence Injection Current plural form, E "iq、E″idFor
D, q axis transient potential, C after motor short circuitix1、Cix2、Ciy1、Ciy2For generator network equation parameter, RiaFor the running fire of node i institute
The internal resistance of motor, δiFor the angle of generator amature q axis and x-axis, X "id、X″iqRespectively d, q axis of node i institute running fire motor
Transient state reactance.
6. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 4, special
Sign is that, when rotating electric machine is motor, network equation expression formula is identical as the expression formula of the network equation of rotating electric machine,
Also,
When motor is double-deck induction motor, then have:
When motor is single mouse cage induction conductivity, then have:
Wherein, RiaFor resistance in the motor in node i, X 'iFor the motor transient state reactance in node i, X "iFor in node i
Motor subtranient reactance, ωi=1-siFor motor angle speed, siFor revolutional slip.
7. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 4, special
Sign is, when rotating electric machine is double-deck induction motor, equivalent Injection Current equation are as follows:
ωi=1-si
Wherein, E "M-id、E″M-iqRespectively connected double-deck induction motor d, q axis of node i time transient potential, Cix、CiyFor net
Network equation parameter, RiaBy the internal resistance of node i even double-deck induction motor, X 'iBy node i even double-deck induction motor
Motor transient state reactance, ωiFor double-deck induction motor angular speed, siFor revolutional slip；
When rotating electric machine is single mouse cage induction conductivity, equivalent Injection Current equation are as follows:
ωi=1-si
Wherein, E'M-iq、E'M-idRespectively node i q, d axis transient potential for connecting single mouse cage induction conductivity, Cix、CiyFor net
Network equation parameter, Ria、X′iThe respectively node i internal resistance, the transient state reactance that connect single mouse cage induction conductivity, ωiFor single mouse cage sense
Induction motor angular speed, siFor single mouse cage motor slip.
8. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 5, special
Sign is, in the step 4), generator decaying potential equation include generator short circuit d axis time transient potential attenuation type and
The attenuation type of q axis time transient potential,
The attenuation type of the generator short circuit q axis time transient potential are as follows:
Wherein, iid0For moment stator winding d shaft current, X before generator short circuitid、X′id、X″idRespectively generator d axis is steady
State reactance, transient state reactance and subtranient reactance, T 'id、T″idFor the time of generator d axis transient state component and time transient state component decaying
Constant, XieFor the ratio of moment generator voltage and generator terminal electric current after generator short circuit, E "iq0For moment q before generator short circuit
Axis transient potential, E "iqFor q axis transient potential after generator short circuit；
When generator q axis direction is there are two Damper Winding, the attenuation type of the generator short circuit d axis time transient potential are as follows:
Wherein, iiq0For moment stator winding q shaft current, X before generator short circuitiq、X′iq、X″iqRespectively generator q axis is steady
State reactance, transient state reactance and subtranient reactance, T 'iq、T″iqFor the time of generator q axis transient state component and time transient state component decaying
Constant, E "idFor d axis transient potential, E " after generator short circuitid0For moment d axis transient potential before generator short circuit,
When generator q only one Damper Winding of axis direction, the attenuation type of the generator short circuit d axis time transient potential
Are as follows:
9. a kind of Power System Shortcuts current attenuation calculation method based on coordinate transform according to claim 7, special
Sign is, in the step 4), motor decaying potential equation includes double-deck induction motor decaying potential equation and list
Mouse cage induction conductivity decaying potential equation,
The attenuation type of the double-deck induction motor short circuit d axis time transient potential and the attenuation type of q axis time transient potential are as follows:
Wherein, iiq0、iid0Moment stator winding q, d shaft current, X respectively before motor short circuitiq、X′iq、X″iqIt is respectively electronic
Steady-state reactance, transient state reactance and the subtranient reactance of machine q axis, Xid、X′id、X″idRespectively the steady-state reactance of motor d axis, temporarily
State reactance and subtranient reactance, T 'iq、T″iqFor the time constant of motor q axis transient state component and time transient state component decaying, T 'id、
T″idFor the time constant of motor d axis transient state component and time transient state component decaying, E "id、E″iqFor d, q axis after motor short circuit
Secondary transient potential, E "id0、E″iq0For moment d, q axis transient potential, X before motor short circuitieIt is electronic for moment after motor short circuit
The ratio of set end voltage and generator terminal electric current；
The attenuation type of single mouse cage induction conductivity short circuit d axis time transient potential and the attenuation type of q axis time transient potential are as follows:
Wherein, E 'iq、E′idWith E 'iq0、E′id0Respectively after motor short circuit and short circuit before moment d, q axis transient potential.
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| CN102646981A (en) * | 2012-04-19 | 2012-08-22 | 上海电力学院 | Power system short-circuit current attenuation practical calculation method |
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